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Braid actions on quantum toroidal superalgebras

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arxiv 1912.08729 v2 pith:YUBHYEEL submitted 2019-12-18 math.QA math-phmath.MP

Luan Bezerra , Evgeny Mukhin This is my paper · ORCID
classification math.QAmath-phmath.MP
keywords mathbfmathcaltoroidalalgebrasbraidquantumactionactions
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abstract

We prove that the quantum toroidal algebras $\mathcal{E}_\mathbf{s}$ associated with different root systems $\mathbf{s}$ of $\mathfrak{gl}_{m|n}$ type are isomorphic. We also show the existence of Miki automorphism of $\mathcal{E}_\mathbf{s}$, which exchanges the vertical and horizontal subalgebras. To obtain these results, we establish an action of the toroidal braid group on the direct sum $\oplus_\mathbf{s} \mathcal{E}_\mathbf{s}$ of all such algebras.

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  1. Weyl Mutations in Quiver Yangians

    hep-th 2026-01 conditional novelty 5.0 of 10

    Weyl group reflections act as Seiberg-like dualities on A_n quiver gauge theories, mapping stability chambers to each other while conjecturally leaving the quiver Yangian Y(sl_{n+1}) invariant.

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